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fallacious
fallacious, a. (fəˈleɪʃəs) [f. L. fallāci-a (see fallacy) + -ous. Cf. F. fallacieux. In early use it appears with sense derived from that of the n.; subsequently (in accordance with the usual tendency of adjs. in -acious) it came to be taken as the representative of L. fallax.] 1. Of an argument, sy...
Oxford English Dictionary
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fallacious
fallacious/fəˈleɪʃəs; fə`leʃəs/ adjmisleading; based on error 令人误解的; 谬误的 fallacious reasoning 错误的推理.
牛津英汉双解词典
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Begging the Question (Petitio Principii): Fallacious Circular Reasoning ...
Begging the question (also called petitio principii or circular reasoning) is a logical fallacy that occurs when an argument's premise depends on or is equivalent to the argument's conclusion. In other words, an argument begs the question if one or more of its premises assume that the argument's conclusion is necessarily true.
effectiviology.com
define fallacious ad hominem
Fallacious ad hominem reasoning occurs where the validity of an argument is not based on an attribute, but on deduction or syllogism.
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A Fallacious Argument on Open Cover of Rationals in $[0,1]$ Let $A=\mathbb{Q}\cap [0,1]$, the set of rational numbers in the interval $[0,1]$, and suppose that $\left(c_{k}\right)_{k=1}^{\infty}$ denotes an ordered en...
There could be uncountably many irrationals not in $\bigcup_{k-1}^{\infty} I_k$ (depending on $\varepsilon$ of course). To see this, let $ \lambda$ denotes the Lebesgue measure on $[0,1]$. Then $\lambda I_k = \frac{\varepsilon}{2^{k-1}}$. Then it would follow that $ \lambda(\bigcup_{k\in\mathbb{N}} ...
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Identify the fallacious argument in the following statement.
False Cause Fallacy; the assumption that immigrants are taking away jobs from American citizens without evidence to suggest a causal relationship.
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I can't remember a fallacious proof involving integrals and trigonometric identities. My calc professor once taught us a fallacious proof. I'm hoping someone here can help me remember it. Here's what I know about it:...
It's probably the classic $$\int \sin 2x \;dx = \int 2\sin x\cos x \;dx$$ * Doing a $u=\sin x$ substitution "gives" $$\int 2u \;du = u^2 = \sin^2 x$$ * Alternatively, using $v = \cos x$ "gives" $$\int -2v \;dv = -v^2 = -\cos^2 x$$ Since the solutions must be equal, we have $$\sin^2 x = -\cos^2 x \qu...
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What are some classic fallacious proofs? If you know it, also try to include the precise reason why the proof is fallacious. To start this off, let me post the one that most people know already: 1. Let $a = b$. ...
Wikipedia has a long list of these: <
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Faulty application of the Fundamental Theorem of Calculus to $f(x) = 0$ for $x\ne 0$, $f(0)=1$ I think I have given a fallacious proof but I can't seem to find what is wrong with it. Suppose $f : \mathbb{R} \rightarr...
The fundamental theorem of calculus states that: > If $f:[a,b]\to\mathbb R$ (say) is a **continuous** function, and we define:
> > $$ F(x)=\int_a^x f(t)dt $$
> > then $F'(x)=f(x)$. I have put one of the words in the statement in **bold** , which is the clue to seeing why the FTC does not apply to yo...
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Circles inscribed in a rectangle are tangent at distinct points; find the radius of the smaller circle based on the dimensions of the rectangle.  states that for a quasi-coherent sheaf $\mathscr F$ on an affine noetherian scheme $H^i(X,\mathscr{F})$ vanish for $i >0$. I used to think that this would...
$GL_n$ is not a coherent sheaf, because it is not a sheaf of $\mathcal{O}_X$-modules.
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Improper proof that $P \neq NP$ > Describe the error in the following fallacious “proof” that $P \neq NP$ . Assume that $P = NP$ and obtain a contradiction. If $P = NP$, then $SAT \in P$ and so for some $k$, $SAT \in ...
Your guess is right. As polynomial time reductions are no necessarily linear time reduction, you cannot get from $SAT\in TIME(n^k)$ that $NP\subseteq TIME(n^k)$. This is because if the reduction runs on $O(n^l)$ time, then the problem (which is reduced to $SAT$) will be solve, in general, in$O(n^{kl...
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A real-world interpretation for $\{\neg(\phi\leftrightarrow\psi)\}\vdash((\neg\phi)\leftrightarrow\psi)$ One of the exercises in Chiswell's _Mathematical Logic_ is to prove the following sequent > $\\{\neg(\phi\leftr...
Rain and precipitation may be thought of as defined by unary predicates $R, P$ respectively true of precisely that which is rain and precipitation. To say that rain is not the same as precipitation essentially means $\neg \forall x (R(x) \leftrightarrow P(x))$. This is equivalent to $\exists x \neg ...
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Multiple "wo"s in a sentence? I had always been told this never happened. I was a little skeptical, but since I never saw a sentence with two of the particle, I gradually came to accept that it was probably true. Wel...
This is a simple case of subclauses - you've still got one per clause: [[]] is the object of , is the object* of . *Depending on your interpretation of with what you would think are intransitive verbs. You can read more about these sorts of cases here: It seems that is categorized as (intransitive v...
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Where is the error in my reasoning about this first-order linear differential equation? Considering this first-order linear differential equation: $\frac{dy}{dx} + 2y = 0$ Although I now know the correct general sol...
Correct way to solve would be $$ \frac {dy}{dx} + 2y = 0 \implies \frac {dy}y = -2dx \implies \int \frac {dy}y = -2\int dx \implies \ln y = -2x + C_1 \implies \\\ y = e^{C_1} e^{-2x} = Ce^{-2x} $$
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